Sum of a Series like the geometric series

Question

This might be a stretch, but I am trying to find the sum of a series similar to the geometric series (Sum of a^j, from j=0 -> j=n); where instead I am trying to find the sum of the series: a^(b^j) from j=0 -> j=n.... Any thoughts?

 

 

Answer 1

Write out the first four terms (can't do exponents with exponents here):
Note that the common ratio is a^b. Substitute it for "r" in the following:

S_n = (1 - rⁿ⁺¹) / (1 - r)